Darlington's Theorem for Rational Nevanlinna Functions in Several Variables
Every rational Nevanlinna function in n variables is a Cayley inner function in n + 1 variables with one variable fixed in the upper half-plane.
math.CV↗
arXiv subjects
M. F. Bessmertnyi
Publications and source records attributed to M. F. Bessmertnyi.
SOS Polynomials and Matrix Representations of Rational Real Functions
The characteristic properties of Artin's denominators in Hilbert's 17th problem are obtained. It is proved that numerators of partial derivative of rational real function from the Nevanlinna class are SOS polynomials.
math.CV↗
Rational Matrix-Valued Pick Functions of Several Variables
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
math.CV↗
Holomorphic Rational Functions of Several Variables and Sums of Squares of Polynomials
Necessary and sufficient conditions are obtained under which the numerator of the partial derivative of a rational function holomorphic in open upper poly-halfplane is the sum of squares of polynomials.
math.CV↗
Representation of rational positive real functions of several variables by means of positive long resolvent
A rational homogeneous (of degree one) positive real matrix-valued function is presented as the Schur complement of a block of the linear pencil with positive semidefinite matrix coefficients. The partial derivative numerators of a rational positive real function are the sums of squares of polynomials.
math.CV↗